论文标题
在白头组和统一之间
Between Whitehead groups and uniformization
论文作者
论文摘要
For a given stationary set $S$ of countable ordinals we prove (in $\mathbf{ZFC}$) that the assertion "every $S$-ladder system has $\aleph_0$-uniformization" is equivalent to "every strongly $\aleph_1$-free abelian group of cardinality $\aleph_1$ with non-freeness invariant $\subseteq S$ is $ \ aleph_1 $ -coseparable，即ext $（g，\ oplus_ {i = 0}^{\ infty} \ mathbb z）= 0 $（尤其是whitehead，即\ ext $（g，\ mathbb z）= 0 $）。这解决了Eklof和Mekler专着的问题B3和B4。
For a given stationary set $S$ of countable ordinals we prove (in $\mathbf{ZFC}$) that the assertion "every $S$-ladder system has $\aleph_0$-uniformization" is equivalent to "every strongly $\aleph_1$-free abelian group of cardinality $\aleph_1$ with non-freeness invariant $\subseteq S$ is $\aleph_1$-coseparable, i.e. Ext$(G, \oplus_{i=0}^{\infty} \mathbb Z)=0$ (in particular Whitehead, i.e.\ Ext$(G, \mathbb Z)=0$)". This solves problems B3 and B4 from Eklof and Mekler's monograph.
